Lever action rifles are usually more compact and able to be carried in high brush country. They will probably never be as accurate as a bolt action, but are often lighter in weight also. They are usually used for larger game such as deer, coyotes, etc. They are usually good "pie pan" size shooters out to 100-150 yards but anything past that is very iffy.
Bolt actions are more accurate, usually heavier, any caliber type guns. They are usually longer, but are good for longer distance shooting.
For long shots out west, you use a bolt action. For deer hunting in the deep brush of the Ozarks, the lever action is the way to go.

If you're looking for a sort of compare and contrast "argument" in favor of one action type or another, I'll argue in favor of a bolt action, for these reasons: bolt guns have inherently better triggers, and most bolt guns have triggers that can be substantially improved by tuning or replacing the factory trigger with an aftermarket --- better trigger = better accuracy. Lever gun triggers can't be made as good. Bolt guns have essentialy two components, barreled action, and one piece stock, inherently more sturdy, rigid, and as a result, again, more accurate. You can get a bolt gun in virtually any chambering you want, whereas lever guns offer a limited selection (may be what you want or need, but it' still limited). Stock shape on bolt guns is designed for scope sights, lever gun stocks are designed for iron sights and most do not adapt well to scope sighting (not to mention ejection interference on top ejectors like Winchester 94s and clones). Bolt guns can be built in ultra light weights, by slimming stocks and using synthetics vs. wood, and paring away excess, non-structural metal (or even, as Remington has done, replacing steel components with titanium alloy). Lever guns are pretty much stuck at original design weight. The most sophisticated modern lever gun designs are simply attempts to achieve bolt gun standards of performance with a much more complex mechanism --- a worthy but unachievable goal. You really need to first define the gun's mission, then set a budget, then see what falls within those brackets. If you're planning to hunt whitetails in the swamp from a blind, with 50 yards a long shot, it's a moot point, you'd do all right with a bow. If you expect to make 400 yard shots on big mule deer, you'll want a rig that's ballistically, optically, and accurately up to job, and if you're gonna lug it over ridge and peak on your shoulder sling, you probably want it to weigh as little as possible, and now you're talking bolt gun.

The lever action came first into the world. Then, as is usual with mechanical design, the concept of the repeater was greatly simplified and parts were integrated, resulting in the bolt action. (there-- decades of history in two sentances)

There are several good reasons to own a lever gun: 1. They're cool. 2. they're handy and fun. 3. You want one. 4. Someone gave you one. And mostly, 5. They're really cool. Then there's 6. They look great on the wall, and 7. You look great carying one, and 8. They look really sharp in the gun rack in the back window of your old rusty pickup.

The lever action came first into the world. Then, as is usual with mechanical design, the concept of the repeater was greatly simplified and parts were integrated, resulting in the bolt action. (there-- decades of history in two sentances)

There are several good reasons to own a lever gun: 1. They're cool. 2. they're handy and fun. 3. You want one. 4. Someone gave you one. And mostly, 5. They're really cool. Then there's 6. They look great on the wall, and 7. You look great carying one, and 8. They look really sharp in the gun rack in the back window of your old rusty pickup.

I think someone is out of the loop when it comes to leveraction rifles;
#1 , The Marlin lever guns often very accurate, some will do moa and better.
#2 The point about lever gun triggers being beyond help, I dont know about Winchester, but Wild West triggers are available from Midway USA and they will give the average Marlin a great chrisp 3lb or less trigger.
#3 I do agree that the Win 94 is much less accurate than most bolt guns, as I've had two and my daughter has one now and they tend to pattern moreso than group.

I think someone is out of the loop when it comes to leveraction rifles;
#1 , The Marlin lever guns often very accurate, some will do moa and better.
#2 The point about lever gun triggers being beyond help, I dont know about Winchester, but Wild West triggers are available from Midway USA and they will give the average Marlin a great chrisp 3lb or less trigger.
#3 I do agree that the Win 94 is much less accurate than most bolt guns, as I've had two and my daughter has one now and they tend to pattern moreso than group.

Tastes great, less filling. Some like chocolate, some like strawberry, some like Glocks. Non gustibus disputandum (Gus missed the bus, dummy)

However, the most popular deer rifles in the US- #1. Winchester 94 in 30-30 #2. Marlin 336 in 30-30.

Would they be my first choice for a 400 yd shot on a Dall sheep? Nope. Hunting in pine woods with honeysuckle thickets? Yep.

And while I would not take it to any matches, my Marlin 39A does a number on squirrels. As far as power, I inherited my uncle's Winchester 71 in .348 Winchester. It will drop anything on this half of the earth.

the lever action came first into the world. Then, as is usual with mechanical design, the concept of the repeater was greatly simplified and parts were integrated, resulting in the bolt action. (there-- decades of history in two sentances)

there are several good reasons to own a lever gun: 1. They're cool. 2. They're handy and fun. 3. You want one. 4. Someone gave you one. And mostly, 5. They're really cool. Then there's 6. They look great on the wall, and 7. You look great carying one, and 8. They look really sharp in the gun rack in the back window of your old rusty pickup.

The main draw back for a lever from a military standpoint was in prone shooting. Also at the time of the shift to bolt, the levers were not up to the high pressures of the bolt loads. Soldiers trained on the bolt made it popular just as the returning soldiers of today made the AR platform popular. The Savage 99, Browning BLR and Marlin are capable of high power loads. All 3 are accurate enough for general hunting. Check out the 338 Marlin Express for one.

The main draw back for a lever from a military standpoint was in prone shooting. Also at the time of the shift to bolt, the levers were not up to the high pressures of the bolt loads. Soldiers trained on the bolt made it popular just as the returning soldiers of today made the AR platform popular. The Savage 99, Browning BLR and Marlin are capable of high power loads. All 3 are accurate enough for general hunting. Check out the 338 Marlin Express for one.

So did Teddy Roosevelt.
I had to sell off almost all my guns one time thanks to political maneuvering taking away my job and any chance of getting one in the area I lived. Among them were several levers. I was at least able to sell my house at 1/3 of what it was worth before the interferance. My wife and I built that house and owned it free and clear or we would have lost it to the bank. I had to carry the note to sell it to a postal worker. 27% unemployment(official rate real was close 50%) and whole shopping centers were shutting down. Divorce rate through the roof and people were just walking away from their houses. Not a fun time and I had to start all over again. A lot of people did. Ask me why I dont trust the goverment.
Sorry for the rant but every time I think about it I get mad and it was 30 years ago.

One other quick thought regarding the lever rifles. Is ammunition restriction regarding they load from a magazine tube. Unless you have ammunition like the new Hornady Soft Point that was made with the lever rifle in mind you can not have pointed projectiles they must be round nose for the biggest part. As was stated for heavy woods and brush guns they are the best due to closer shots and they are compact. I like the lever guns also since I have a Marlin as well as a 94 Winchester and one of my favorites a Marlin 39-A 22 cal. rifle. Just a consideration when it comes to ammunition and improved ballistics the boat tailed bullets and various others afford. I think the new Hornady rounds are great when it comes to the levers.